Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1198 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 275 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C22⋊(C71⋊C16) | C2 | semidirect |
| 3. C22×C71⋊C16 | C22 | semidirect |
| 25. C24×C71 | C16 | semidirect |
| 66. C22×C71 | C22⋊C16 | semidirect |
| 80. C71 | #12679 | semidirect |
| 102. C24 | C71⋊C16 | semidirect |
| 144. C22 | C22⋊(C71⋊C16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C71⋊C16) | 2 |
| C24×C8×C71 | 2 |
| #12679 | 71 |